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Precipitation prediction of numerical analysis for Mg-Al alloys
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β τ - iv -
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β β Δ τ - vi -
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국문요약 - ix -
영문요약 - x -
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Ω - 2 -
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핵성장시부피분율계산 exp - 7 -
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f = é 1- exp ù ç æ - ö êë è ò t J ( t ) V ( t, t ) dt 0 øúû f é ù eq æ 1 ö = f ê1 - expç- ò t J ( t ) V ( t, t ) dt eq ú ë è f 0 øû Δ - 9 -
J = N V * æ DG ö æ t ö Zb exp ç- expç - è kbt ø è t ø β τ τ τ - 10 -
Δ γ Δ D Ghom = -V ( DGv - DGs ) + Ag ϒ DG hom 4 = - p r 3 3 ( DG v - DG s 2 ) + 4p r g - 11 -
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Δ d( DG) = 0 dr r * = 2g ( DG v - DG s ) Δ Δ DG * 3 16pg = 3( DG V - DG S ) 2 Δ Δ Δ β O b a ( X ) a( X ) + a( X B B b B ) G hom = 4/3πr 3 G v + 4πr 2 g Δ Δ DG V = DG V m n Δ - 13 -
Δ Δ Δ DG 1 = b X A m - X O A b B m O B Δ X O X b DG 2 = b X A m - X e A b B m e B Δ β Fig 3. The change of gibbs energy - 14 -
N V æ l ö = ç è d ø 3-M æ ç è N V 0 ö ø λ - 15 -
π γ π γ - 16 -
β β 2 * 16pg DXL b = 4 a D 2 G V γ Δ Z = VmDG 2 V 3 8p ( ktkg ) 1 2-17 -
* DG DG * 3 16pg = 3( D ) G V 2 τ t = 4 12kTa g DX ( 2 V m ) ( DG V ) 2 γ - 18 -
β γ - 19 -
α v = dx dt = C b D - C e dc dx DC / 0 L( DC0 = C - C ) 0 e ( C b DC - C0 ) x = L 2 0 v = DDC0 2( CB - Ce )( CB - C0 ) x 2 DX x = ( X - X b ( DT ) 0 2 ) 1/ e - 20 -
v = DX 0 2( X - X b e æ ç ) è D t ö ø 1/ 2 æ Q D = D0 expç - è RT ö ø - 21 -
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r 3 3 g 0 - r 8 DCm ( V = 9RT m ) 2 t r 2 2 g 0 - r 64 DCm ( V = 81RT m ) 2 t γ - 23 -
β β C r æ 2gVm = C expç è RTr ö ø γ - 24 -
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α - 26 -
ln ln - 27 -
ln - 28 -
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ln ln - 30 -
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Φ - 32 -
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μ - 34 -
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β - 36 -
τ τ τ τ β τ - 37 -
. Δ Δ Δ Δ Δ Δ - 38 -
Δ Δ Δ Δ Δ Δ - 39 -
T(K) T( ) μ(aα)(j) X(A) μ(bα)(j) X(B) G 2 (J) 353 80-11825.3 0.585962-10735 0.414038-13464.2 393 120-13386.8 0.586018-13014.7 0.413982-15001.6 425 152-14713 0.586212-14914.3 0.413788-16311 473 200-16820.4 0.586873-17880.5 0.413127-18398.7 521 248-19058.9 0.588129-20976.7 0.411871-20626 577 304-21823 0.590521-24740.7 0.409479-23390.2 T(K) T( ) μ(aα)(j) X(A) μ(bα)(j) X(B) G 2 (J) 353 80-11346.8 0.414038-11781.5 0.585962-13464.2 393 120-13333.8 0.586018-13755.4 0.413982-15001.6 425 152-14652.5 0.586212-15758.2 0.413788-16311 473 200-16748.8 0.586873-18879.1 0.413127-18398.7 521 248-18976.2 0.588129-22130 0.411871-20626 T(K) T( ) μ(aα)(j) X(A) μ(bα)(j) X(B) G 2 (J) 353 80-12689 0.439595-12689 0.439595-13464.2 393 120-13270.8 0.560463-15321.3 0.439537-15001.6 425 152-14582.2 0.560659-17503 0.439341-16311 - 40 -
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Δ Δ Δ Δ Δ Δ Δ Δ Δ τ τ - 42 -
τ - 43 -
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Number density of site for Mg 17 Al 12 : Nv 8.8910 17 /m 3 Interfacial energy of Mg 17 Al 12 : ϒ 0.01 J/m 3 Volume diffusion coefficient for Al: D 0 1.210-3 m 2 /s Activation energy for volume diffusion: Q 144 KJ/mol Lattice parameter of Mg 17 Al 12 : a 10.54 nm (a) Mg-9Al T( ) r*(nm) G * (x10-21 J) τ (sec) 80 0.11 0.567 127904 120 0.137 0.791 620 152 0.161 1.07 16.48 200 0.213 1.9 0.149 248 0.312 4.1 0.0023 304 0.65 17.8 2.16x10-5 (b) Mg-6Al (c) Mg-3Al T( ) r * (nm) G * (x10-21 J) τ (sec) 80 0.13 0.714 101559 120 0.16 1.11 442.479 153 0.2 1.74 9.2764 200 0.315 4.18 0.06810 248 0.69 20.1 4.8x10-4 T( ) r * (nm) G * (x10-21 J) τ (sec) 80 0.18 1.43 50538 120 0.29 3.6 136.56 153 0.56 13.2 1.228-45 -
(a)mg-9al Incubation time (τ- sec) Nucleation rate (J - #/m 2 s) 96 13414.85 2.9216x10 13 120 620 6.19x10 14 152 16.49 2.24x10 16 (b)mg-6al Incubation time (τ- sec) Nucleation rate (J - #/m 2 s) 75 215904 1074503.483 100 5932.1468 6.319x10 13 245 6.77x10-4 5.714x10 19 (c)mg-3al Incubation time (τ- sec) Nucleation rate (J - #/m 2 s) 100 2419.232 1.21x10 14 156 0.77765 4.06846x10 16-46 -
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본연구는 - 56 -
4) C. D. Lee and C. S. Kang, J. Kor. Inst. Met. & Mater. Vol.39, No.1 (2001) - 57 -